Symmetry of hypergeometric functions over finite fields and geometric interpretation
Number Theory
2026-04-22 v4
Abstract
We begin by defining general hypergeometric functions over finite fields and obtaining a finite field analogue of a classical symmetry in their complex counterparts. We give a geometric proof for the symmetry by constructing isomorphisms between certain algebraic varieties. The numbers of rational points on these varieties are hypergeometric functions over finite fields.
Keywords
Cite
@article{arxiv.2505.05858,
title = {Symmetry of hypergeometric functions over finite fields and geometric interpretation},
author = {Akio Nakagawa},
journal= {arXiv preprint arXiv:2505.05858},
year = {2026}
}
Comments
45 pages